Question

Phil makes and sells rugs at his roadside stand. His monthly fixed cost for owning the stand is $1035. If he makes and sells 18 rugs, his total costs are $1179 and he brings in $558 in revenue. Find Phil's monthly cost, revenue, and profit functions (assuming they are linear). Let x be the number of rugs made and sold each month.

Answer 1

Total fixed cost = $1035

Rugs sells = 18

Total costs = $1179

Revenue = $558

Total variable cost = Total costs - Total fixed cost

= $1179 - $1035

= $144 for 18 rugs

`Variable\ cost\ per\ rug = (144)/(18)`

= $8 per rug

Where,

x represents number of rugs

C(x) = $1035 + 8x ⇒ Cost function

Revenue for 18 rugs = $558

`Revenue\ per\ rug = (558)/(18)`

= $31 per rug

R(x) = 31x ⇒ Revenue Function

Profit = revenue - cost

P(x) = 31x - (1035 + 8x)

= 31x - 1035 - 8x

= 23x - 1035 ⇒ Profit Function